Answer
See the detailed answer below.
Work Step by Step
We are given that,
- $\vec E=( 2\times10^5\;\hat i-2\times 10^5\;\hat j)\;\rm V/m$
- $\vec v= ( 5\times 10^6\;\hat i)\;\rm m/s$
- $\vec B=(-0.1\;\hat k)\;\rm T$
Recalling that the net force exerted on a moving charge in an electromagnetic field is given by
$$\sum F=q(\vec E+\vec v\times \vec B)$$
So, the net force exerted on an electron is given by
$$\sum F=e(\vec E+\vec v\times \vec B)$$
Plug the known;
$$\sum F=(-1.6\times 10^{-19})[( 2\times10^5\;\hat i-2\times 10^5\;\hat j)+( 5\times 10^6\;\hat i) \times (-0.1\;\hat k)]$$
$$\sum F=(-1.6\times 10^{-19})[ 2\times10^5\;\hat i-2\times 10^5\;\hat j + 5\times 10^5\;\hat j ]$$
$$\sum F=(-1.6\times 10^{-19}) [(2\times10^5)\;\hat i+(3\times10^5)\;\hat j]$$
$$\sum F=(-\color{red}{\bf 3.2\times 10^{-14}}\;\hat i -\color{red}{\bf 4.8\times 10^{-14}}\;\hat j)\;\rm N$$
